## Graduate Faculty and Their Research

**Jeffrey Brock [1]**,

**Ph.D., U.C. Berkeley 1997. Guggenheim Fellow, AMS Fellow. Dean of the School of Engineering and Applied Science.**Hyperbolic geometry, low dimensional topology, and applications.

**Andrew Casson [2]**,

**Cambridge University, 1969. Royal Society Fellow. (Emeritus)**Low-dimensional topology, four manifold theory, algebraic topology, hyperbolic geometry.

**Ronald Coifman [3]**,

**Ph.D., Geneva, 1965. Philips Professor of Mathematics, National Academy of Sciences, American Academy of Arts and Sciences, National Medal of Science, Rolf Schock prize .**Nonlinear analysis, Scattering theory, Real and complex analysis, Singular integrals, Numerical analysis, Harmonic analysis and Geometry in high dimension Data Analysis

**Students:**

**Igor Frenkel [4]**,

**Ph.D., Yale, 1980. American Academy of Arts and Sciences and National Academy of Sciences.**Infinite-dimensional algebras, representation theory, applications of Lie theory, mathematical physics.

**Anna Gilbert [5]**,

**Ph.D., Princeton, 1997.**Analysis, probability, discrete mathematics, (randomized) algorithms with applications to harmonic analysis, signal and image processing, and massive datasets

**Students:**

**Alexander Goncharov [6]**,

**Ph.D., (USSR) 1987. European Mathematical Society Prize.**Arithmetic Algebraic Geometry: polylogarithms, zeta-functions, periods, Hodge theory, motives, motivic Galois groups, Quantum geometry of moduli spaces, Representation Theory and Mathematical Physics

**Sebastian Hurtado - Salazar [7]**,

**Ph.D., University of California Berkeley, 2014.**Dynamical systems and its applications to geometry and topology. Groups actions on manifolds. Discrete subgroups of Lie groups.

**Peter Jones [8]**,

**Ph.D., UCLA, 1978. American Academy of Arts and Sciences. National Academy of Sciences. Salem Prize.**Real, complex, and Fourier analysis, singular integrals, potential theory, dynamical systems.

**Richard Kenyon [9]**,

**Ph.D., Princeton, 1990. Loeve Prize, Rollo Davidson Prize, American Academy of Arts and Sciences.**Combinatorics, Discrete Geometry, Probability, Statistical Mechanics.

**Students:**

**Ivan Loseu [10]**,

**Ph.D., Moscow State University, 2007.**Representation theory and its connections to Algebraic and Symplectic Geometry and to Combinatorics.

**Students:**

**Gregory Margulis [11]**,

**Ph.D., Moscow, 1970. American Academy of Arts and Sciences. National Academy of Sciences. Fields Medal. Abel Prize. (Emeritus)**Lie group theory, ergodic theory, number theory, network theory, and dynamics.

**Yair Minsky [12]**,

**Ph.D., Princeton University, 1989.**Kleinian groups, Teichmuller theory, geometric group theory, holomorphic dynamics, differential geometry.

**Students:**

**Andrew Neitzke [15]**,

**Ph.D., Harvard, 2005.**Supersymmetric quantum field theory, string theory, enumerative geometry, hyperkahler geometry

**Students:**

**Hee Oh [16]**,

**Ph.D., Yale, 1997. Satter Prize.**Homogeneous dynamics, discrete subgroups of Lie groups, Kleinian groups, hyperbolic geometry, and the resulting applications of number theory.

**Students:**

**Vladimir Rokhlin [19]**,

**Ph.D., Rice, 1983. National Academy of Sciences.**Numerical scattering theory, elliptic partial differential equations, numerical solution of integral equations.

**Wilhelm Schlag [20]**,

**Ph.D., Caltech 1996. Philips Professor of Mathematics**Spectral Theory, Partial differential evolution equations, harmonic analysis

**Students:**

**John Schotland [22]**,

**M.D., Ph.D., University of Pennsylvania, 1996**Inverse problems, scattering theory, waves in random media, quantum optics.

**Junliang Shen [23]**,

**Ph.D., ETH Zurich 2018.**Algebraic geometry and its connections to topology, enumerative geometry, and mathematical physics.

**Students:**

**Van Vu [25]**,

**Ph.D., Yale, 1998. Polya Prize. Fulkerson Prize.**Combinatorics, probability, additive number theory, data science.

**Students:**

**Gregg Zuckerman [27]**,

**Ph.D., Princeton, 1975. (Emeritus)**Representation theory, applications of Lie theory, mathematical physics.